The machine in the video doesn't use typical units, so it is hard to understand what they measure.
Assuming the power output (##51064\ lb.ft/s##) and the reaction time (##0.13224\ s##) are right I found this
human punch calculator that could help you. Not only it is a calculator but the equations used are all described.
The force ##F## is related to the mass ##m## of the boxer and the accelaration of the punch ##a##:
$$F= ma$$
Where the acceleration is related to the maximum speed ##v## of the punch and the time ##t## it takes to decelerate to a stop:
$$F= m\frac{v}{t}$$
As we said earlier, the power is the force times the average velocity ##v_{avg}##:
$$P = Fv_{avg}$$
Since the initial velocity is the maximum velocity of the punch and the final velocity is zero, then ##v_{avg} = \frac{v}{2}##. Thus:
$$P = \left( m\frac{v}{t} \right) \left( \frac{v}{2} \right) = \frac{\frac{1}{2}mv^2}{t}$$
Which corresponds to the kinetic energy of the boxer's body released during the reaction time period. Seems logical.
Let's find out the initial speed of the punch:
$$v = \sqrt{\frac{2Pt}{\left( \frac{W}{g} \right)}} = \sqrt{\frac{2(51064\ lb.ft/s)(0.13224\ s)}{\left( \frac{250\ lb}{32.174\ ft/s^2} \right)}} = 41.7\ ft/s$$
Here I use ##W = mg## to be able to use the weight ##W## of the boxer (I guessed a ##250\ lb## value). ##g## is the acceleration due to gravity. According to
this source, ##41.7\ ft/s## (##28\ mph##) is a reasonable assumption:
Therefore:
$$F = \left(\frac{W}{g}\right)\frac{v}{t} = \left(\frac{250\ lb}{32.174\ ft/s^2}\right)\frac{41.7\ ft/s}{0.13224\ s} = 2450\ lb \equiv 10899\ N$$
Which is the result you would get with the human punch calculator presented above.
This is how I would "convert" 51064 foot-pounds per second to Newtons in this particular scenario.